That isn't my own list - that is the list on Heathrow's own website. I am extremely sceptical on many of those destinations, but that said most would likely only be operated by home carriers.
Re Auckland (not already operated by ANZ?) - EK can barely make it profitable from DXB with all their advantages, let alone on a 1-stop from LHR. You're burning more fuel just carrying it. On that subject, I note that the inaugural PER-LHR leg was done with 94T on the 787 with another hours flying time available; not as high as I was expecting.
For me, the following will be operated from LHR pretty quickly:
UK & Ireland: Jersey, Guernsey, Cardiff, Isle of Man, Liverpool, Newquay, Derry, Knock
Europe: Alicante, Naples, Porto, Valencia, Bordeaux, Heraklion, Seville, Dubrovnik (a lot served by an EZY hub)
North America: Orlando, Cancun, Memphis, Bermuda, St Lucia, Punta Cana, San Jose de Costa Rica, Port-of-Spain
South America: Quito, Lima
Africa: Dakar, Entebbe, Dar es Salaam, Khartoum
Middle East: Baghdad, Damascus (eventually), Erbil
South Asia: Goa, Kolkata
China: Chengdu, Shenzhen, Chongqing, Nanjing, Xiamen, Tianjin
Far East: Osaka
Oceania: Brisbane
Potential new entrants (airlines):
Air Transat, easyJet, Iraqi Airways, Montenegro Airlines, Nouvelair, Tianjin Airlines, Xiamen Airlines, Wizz Air